Chapter 13. Properties of Solutions 13.1 The Solution Process A solution is a homogeneous mixture of solute and solvent. Solutions may be gases, liquids, or solids, Each substance present is a component of the solution. The solvent is the component present in the largest amount. The other components are the solutes. The Natural Tendency Toward Mixing Consider the formation of a gaseous solution of O 2 (g) and Ar(g). The mixing of gases is a spontaneous process. It occurs without input of energy from the surroundings. Entropy is the thermodynamic quantity that measures the extent of the spreading of the molecules and their associated kinetic energies. The mixing that occurs as the solution is formed represents an increase in entropy. Formation of a solution is favored by the increase in entropy that accompanies mixing. The Effect of Intermolecular Forces on Solution Formation Intermolecular forces become rearranged in the process of making solutions with condensed phases. Intermolecular forces operate between solute and solvent particles in a solution. Three kinds of intermolecular interactions are involved in solution formation: Solute-solute interactions between solute particles. These must be overcome in order to disperse the particles through the solvent. Solvent-solvent interactions between solvent particles. These must be overcome to make room for the solute particles in the solvent. Solvent-solute interactions between solvent and solute particles. These occur as the particles mix. Consider NaCl (solute) dissolving in water (solvent): Water molecules orient themselves on the NaCl crystals. H-bonds between the water molecules have to be broken. NaCl dissociates into Na + and Cl. Ion-dipole forces form between the Na + and the negative end of the water dipole. Similar ion-dipole interactions form between the Cl and the positive end of the water dipole. Such an interaction between solvent and solute is called solvation. If water is the solvent, the interaction is called hydration. Energetics of Solution Formation There are three steps involving energy in the formation of a solution: Separation of solute molecules ( H solute ), Separation of solvent molecules ( H solvent ), and Formation of solute-solvent interactions ( H mix ). We define the enthalpy change in the solution process as: H soln = H solute + H solvent + H mix H soln can either be positive or negative, depending on the intermolecular forces. To determine whether H soln is positive or negative, we consider the strengths of all solute-solute, solventsolvent, and solute-solvent interactions: Breaking attractive intermolecular forces is always endothermic. H solute and H solvent are both positive. Forming attractive intermolecular forces is always exothermic. H mix is always negative. It is possible to have either H mix > ( H solute + H solvent ) or H mix < ( H solute + H solvent ).
Examples: MgSO 4 added to water has H soln = 91.2 kj/mol. NH 4 NO 3 added to water has H soln = + 26.4 kj/mol. MgSO 4 is often used in instant heat packs and NH 4 NO 3 is often used in instant cold packs. How can we predict if a solution will form? In general, solutions form if the H soln is negative. If H soln is too endothermic, a solution will not form. Rule of thumb : polar solvents dissolve polar solutes. Nonpolar solvents dissolve nonpolar solutes. Consider the process of mixing NaCl in gasoline. Only weak interactions are possible because gasoline is nonpolar. These interactions do not compensate for the separation of ions from one another. Result: NaCl doesn't dissolve to any great extent in gasoline. Consider the process of mixing a polar liquid solute (water ) with a nonpolar liquid solvent (octane (C 8 H 18 )). Water has strong H-bonds. The energy required to break these H-bonds is not compensated for by interactions between water and octane. Result: water and octane do not mix. Solution Formation and Chemical Reactions Some solutions form by physical processes and some by chemical processes. Consider: Ni(s) + 2HCl(aq) NiCl 2 (aq) + H 2 (g) Note that the chemical form of the substance being dissolved has changed during this process (Ni NiCl 2 ) When all the water is removed from the solution, no Ni is found, only NiCl 2 6H 2 O remains. Therefore, the dissolution of Ni in HCl is a chemical process. By contrast: NaCl(s) + H 2 O (l) Na + (aq) + Cl (aq). When the water is removed from the solution, NaCl is found. Therefore, NaCl dissolution is a physical process. 13.2 Saturated Solutions and Solubility As a solid dissolves, a solution forms: Solute + solvent solution The opposite process is crystallization. Solution solute + solvent If crystallization and dissolution are in equilibrium with undissolved solute, the solution is saturated. There will be no further increase in the amount of dissolved solute. Solubility is the amount of solute required to form a saturated solution. A solution with a concentration of dissolved solute that is less than the solubility is said to be unsaturated. A solution is said to be supersaturated if more solute is dissolved than in a saturated solution. 13.3 Factors Affecting Solubility The tendency of a substance to dissolve in another depends on: the nature of the solute. the nature of the solvent. the temperature. the pressure (for gases). Solute-Solvent Interactions Intermolecular forces are an important factor in determining solubility of a solute in a solvent. The stronger the attraction between solute and solvent molecules, the greater the solubility. For example, polar liquids tend to dissolve in polar solvents. Favorable dipole-dipole interactions exist (solute-solute, solvent-solvent, and solute-solvent). Pairs of liquids that mix in any proportions are said to be miscible. Example: Ethanol and water are miscible liquids. In contrast, immiscible liquids do not mix significantly.
Example: Gasoline and water are immiscible. Consider the solubility of alcohols in water. Water and ethanol are miscible because the broken hydrogen bonds in both pure liquids are re-established in the mixture. However, not all alcohols are miscible with water. Why? The number of carbon atoms in a chain affects solubility. The greater the number of carbons in the chain, the more the molecule behaves like a hydrocarbon. Thus, the more C atoms in the alcohol, the lower its solubility in water. Increasing the number of OH groups within a molecule increases its solubility in water. The greater the number of OH groups along the chain, the more solute-water H-bonding is possible. Generalization: like dissolves like. Substances with similar intermolecular attractive forces tend to be soluble in one another. The more polar bonds in the molecule, the better it dissolves in a polar solvent. The less polar the molecule the less likely it is to dissolve in a polar solvent and the more likely it is to dissolve in a nonpolar solvent. Network solids do not dissolve because the strong intermolecular forces in the solid are not reestablished in any solution. Pressure Effects The solubility of a gas in a liquid is a function of the partial pressure of the gas over the solution. Solubilities of solids and liquids are not greatly affected by pressure. With higher gas pressure, more molecules of gas are close to the surface of the solution and the probability of a gas molecule striking the surface and entering the solution is increased. Therefore, the higher the pressure, the greater the solubility. The lower the pressure, the smaller the number of molecules of gas close to the surface of the solution resulting in a lower solubility. Henry's law. The solubility of a gas in a liquid solvent is directly proportional to the partial pressure of the gas above the solution. Henry's law may be expressed mathematically as: S g =kp g Where S g is the solubility of gas, P g the partial pressure, k = Henry s law constant. Note that the Henry's law constant differs for each solute-solvent pair and differs with temperature. An application of Henry's law is the preparation of carbonated soda. Carbonated beverages are bottled under P CO2 > 1 atm. As the bottle is opened, P CO2 decreases and the solubility of CO 2 decreases. Therefore, bubbles of CO 2 escape from solution. Temperature Effects Experience tells us that sugar dissolves better in warm water than in cold water. The solubility of most solid solutes in water increases as the solution temperature increases. Sometimes solubility decreases as temperature increases (e.g., Ce 2 (SO 4 ) 3 ). Experience tells us that carbonated beverages go flat as they get warm. The solubility of gas in water decreases with increasing temperature. An environmental application of this is thermal pollution. Thermal pollution: if lakes get too warm, CO 2 and O 2 become less soluble and are not available for plants or animals. Fish suffocate. 13.4 Expressing Solution Concentration All methods involve quantifying the amount of solute per amount of solvent (or solution). Concentration may be expressed qualitatively or quantitatively. The terms dilute and concentrated are qualitative ways to describe concentration. A dilute solution has a relatively small concentration of solute. A concentrated solution has a relatively high concentration of solute.
The most commonly used expressions for concentration are: mass percentage. mole fraction. molarity. molality. Mass Percentage, ppm, and ppb Mass percentage is one of the simplest ways to express concentration. By definition: Mass % of component mass of component in soln totalmass of solution Similarly, parts per million (ppm) can be expressed as the number of mg of solute per kilogram of solution. By definition: Partsper million (ppm)of component totalmass of solution The density of a very dilute aqueous solution is similar to that of pure water (1g/mL) If the density of the solution is 1g/mL, then 1 ppm = 1 mg solute per liter of solution. We can extend this again! Parts per billion (ppb) can be expressed as the number of µg of solute per kilogram of solution. By definition: mass of component in soln Partsper billion (ppb)of component 10 totalmass of solution If the density of the solution is 1g/mL, then 1 ppb = 1 µg solute per liter of solution. Mole Fraction, Molarity, and Molality Common expressions of concentration are based on the number of moles of one or more components. Recall that mass can be converted to moles using the molar mass. Recall: Molefractionof component, X Note that mole fraction has no units. Note that mole fractions range from 0 to 1. Recall: molesof solute Molarity, M litersof solution Note that molarity will change with a change in temperature (as the solution volume increases or decreases). We can define molality (m), yet another concentration unit: molesof solute Molality, m kilogramsof solvent Molality does not vary with temperature. Note that converting between molarity (M) and molality (m) requires density. The molarity and molality of dilute solutions are often very similar. 13.5 Colligative Properties Colligative properties depend on number of solute particles. There are four colligative properties to consider: vapor pressure lowering (Raoult's law). boiling point elevation. freezing point depression. osmotic pressure. 100 massof component in soln molesof component totalmolesof allcomponents 6 10 9
Vapor-Pressure Lowering Consider a volatile liquid in a closed container. After a period of time, an equilibrium will be established between the liquid and its vapor. The partial pressure exerted by the vapor is the vapor pressure. Nonvolatile solutes (with no measurable vapor pressure) reduce the ability of the surface solvent molecules to escape the liquid. Therefore, vapor pressure is lowered. The amount of vapor pressure lowering depends on the amount of solute. Raoult s law quantifies the extent to which a nonvolatile solute lowers the vapor pressure of the solvent. If P solution is the vapor pressure of the solution, P solvent is the vapor pressure of the pure solvent, and solute is the mole fraction of solute, then o P solution X solvent P solvent The vapor-pressure lowering, P, is directly proportional to the mole fraction of the solute, solute. o P X solute P solvent An ideal solution is one that obeys Raoult s law. Real solutions show approximately ideal behavior when: the solute concentration is low. the solute and solvent have similarly sized molecules. the solute and solvent have similar types of intermolecular attractions. Raoult s law breaks down when the solvent-solvent and solute-solute intermolecular forces are much greater or weaker than solute-solvent intermolecular forces. Boiling-Point Elevation A nonvolatile solute lowers the vapor pressure of a solution. At the normal boiling point of the pure liquid, the solution has a has a vapor pressure less than 1 atm. Therefore, a higher temperature is required to reach a vapor pressure of 1 atm for the solution ( T b ). The molal boiling-point-elevation constant, K b, expresses how much T b changes with molality, m: T b = K b m The nature of the solute (electrolyte vs. nonelectrolyte) will impact the colligative molality of the solute. Freezing-Point Depression When a solution freezes, crystals of almost pure solvent are formed first. Solute molecules are usually not soluble in the solid phase of the solvent. Therefore, the triple point occurs at a lower temperature because of the lower vapor pressure for the solution. The melting-point (freezing-point) curve is a vertical line from the triple point. Therefore, the solution freezes at a lower temperature ( T f ) than the pure solvent. The decrease in freezing point ( T f ) is directly proportional to molality. K f is the molal freezing-point-depression constant. T f = K f m Values of K f and K b for most common solvents can be found in Table 13.4. Osmosis Semipermeable membranes permit passage of some components of a solution. Often they permit passage of water but not larger molecules or ions. Examples of semipermeable membranes are cell membranes and cellophane. Osmosis is the net movement of a solvent from an area of low solute concentration to an area of high solute concentration. Consider a U-shaped tube with a two liquids separated by a semipermeable membrane. One arm of the tube contains pure solvent. The other arm contains a solution. There is movement of solvent in both directions across a semipermeable membrane. As solvent moves across the membrane, the fluid levels in the arms become uneven. The vapor pressure of solvent is higher in the arm with pure solvent.
Eventually the pressure difference due to the difference in height of liquid in the arms stops osmosis. Osmotic pressure,, is the pressure required to prevent osmosis. Osmotic pressure obeys a law similar in form to the ideal-gas law. For n moles, V= volume, M= molarity, R= the ideal gas constant, and an absolute temperature, T, the osmotic pressure is: RT MRT Two solutions are said to be isotonic if they have the same osmotic pressure. Hypotonic solutions have a lower, relative to a more concentrated solution. Hypertonic solutions have a higher, relative to a more dilute solution. We can illustrate this with a biological system: red blood cells. Red blood cells are surrounded by semipermeable membranes. If red blood cells are placed in a hypertonic solution (relative to intracellular solution), there is a lower solute concentration in the cell than the surrounding tissue. Osmosis occurs and water passes through the membrane out of the cell. The cell shrivels up. This process is called crenation. If red blood cells are placed in a hypotonic solution, there is a higher solute concentration in the cell than outside the cell. Osmosis occurs and water moves into the cell. The cell bursts (hemolysis). To prevent crenation or hemolysis, IV (intravenous) solutions must be isotonic relative to the intracellular fluids of cells. Everyday examples of osmosis include: If a cucumber is placed in NaCl solution, it will lose water to shrivel up and become a pickle. A limp carrot placed in water becomes firm because water enters via osmosis. Eating large quantities of salty food causes retention of water and swelling of tissues (edema). Water moves into plants, to a great extent, through osmosis. Salt may be added to meat (or sugar added to fruit) as a preservative. Salt prevents bacterial infection: A bacterium placed on the salt will lose water through osmosis and die. Active transport is the movement of nutrients and waste material through a biological membrane against a concentration gradient. Movement is from an area of low concentration to an area of high concentration. Active transport is not spontaneous. Energy must be expended by the cell to accomplish this. Determination of Molar Mass Any of the four colligative properties may be used to determine molar mass. n V 13.6 Colloids Colloids or colloidal dispersions are suspensions in which the suspended particles are larger than molecules but too small to separate out of the suspension due to gravity. Particle size: 5 to 1000 nm. A colloid particle may consist of a single giant molecule. Example: hemoglobin has molecular dimensions of 6.5 5.5 5.0 nm and a molar mass of 64,500 g/mol. There are several types of colloids: aerosol: gas + liquid or solid (e.g., fog and smoke), foam: liquid + gas (e.g., whipped cream), emulsion: liquid + liquid (e.g., milk), sol: liquid + solid (e.g., paint), solid foam: solid + gas (e.g., marshmallow), solid emulsion: solid + liquid (e.g., butter), solid sol: solid + solid (e.g., ruby glass).
The Tyndall effect is the ability of colloidal particles to scatter light. The path of a beam of light projected through a colloidal suspension can be seen through the suspension. Hydrophilic and Hydrophobic Colloids Focus on colloids in water. Water-loving colloids are hydrophilic. Water-hating colloids are hydrophobic. In the human body, large biological molecules such as proteins are kept in suspension by association with surrounding water molecules. These macromolecules fold up so that hydrophobic groups are away from the water (inside the folded molecule). Hydrophilic groups are on the surface of these molecules and interact with solvent (water) molecules. Typical hydrophilic groups are polar (containing C O, O H, N H bonds) or charged. Hydrophobic colloids need to be stabilized in water. One way to stabilize hydrophobic colloids is to adsorb ions on their surface. Adsorption: when something sticks to a surface, we say that it is adsorbed. If ions are adsorbed onto the surface of a colloid, the colloid appears hydrophilic and is stabilized in water. Consider a small drop of oil in water. Add a small amount of sodium stearate. Sodium stearate has a long hydrophobic hydrocarbon tail and a small hydrophilic head. The hydrophobic tail can be absorbed into the oil drop, leaving the hydrophilic head on the surface. The hydrophilic heads then interact with the water and the oil drop is stabilized in water. A soap acts in a similar fashion. Soaps are molecules with long hydrophobic tails and hydrophilic heads that remove dirt by stabilizing the colloid in water. Most dirt stains on people and clothing are oil-based. Biological application of this principle: The gallbladder excretes a fluid called bile. Bile contains substances (bile salts) that form an emulsion with fats in our small intestine. Emulsifying agents help form an emulsion. Emulsification of dietary fats and fat-soluble vitamins is important in their absorption and digestion by the body. Removal of Colloid Particles We often need to separate colloidal particles from the dispersing medium. This may be problematic. Colloid particles are too small to be separated by physical means (e.g., filtration). However, colloid particles often may be coagulated (enlarged) until they can be removed by filtration. There are various methods of coagulation. Colloid particles move more rapidly when the colloidal dispersion is heated, increasing the number of collisions. The particles stick to each other when they collide. Adding an electrolyte neutralizes the surface charges on the colloid particles. A biological application of another approach to separating colloidal particles from the suspending medium is dialysis. In dialysis, a semipermeable membrane is used to separate ions from colloidal particles. In kidney dialysis, the blood is allowed to pass through a semipermeable membrane immersed in a washing solution. The washing solution is isotonic in ions that must be retained. The washing solution does not have the waste products that are found in the blood. Wastes therefore dialyze out of the blood (move from the blood into the washing solution). The "good" ions remain in the blood. Selected Problems: 15, 17, 23, 27, 29, 33, 39,41, 43, 45, 47, 51, 53, 55, 59, 63, 65, 67, 68, 69, 71, 73, 75, 77, 81, 83.